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The number of ways of constructing questions from the pool of 28 questions if her test is to have 3 difficult, 4 average and 3 easy questions is 924, 000 ways
<h3>How to determine the combination</h3>Note that the formula for combination is given as;
Combination =
From the information we have that;
There are 28 questions in the pool
The test should have a total of 10 questions;
6 difficult , 10 average and 12 easy questions
We are asked to determine the combination of;
3 difficult questions
4 average questions
3 easy questions
6C3 =
6C3 =
6C3 = 20
10C4 =
10C4 =
10C4 = 210
12C4 =
12C4 = 220
The number of ways of constructing the questions is
= 20 × 210 × 220
= 924, 000 ways
Thus, the number of ways of constructing questions from the pool of 28 questions if her test is to have 3 difficult, 4 average and 3 easy questions is 924, 000 ways
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2(x + 4) =
x + 4 which is the second option is the equivalent expression.
Explanation:
First, we need to calculate the value of two-fifths of x. It means 2 portions out of the five portions of x which equates to x.
Now we calculate the values of the two expresssions on the LHS.
1) 2 (two-fifths x + 2) = 2 (x + 2) =
x + 4.
2) (two-fifths x + 4) = 2(x + 4) =
x + 8.
Now we determine values of the four expressions on the RHS.
1) Two and two-fifths x + 1 = 2x + 1
2) Four-fifths x + 4 = x + 4
3) Four-fifths x + 2 = x + 2
4) Two and two-fifths x + 8 = 2x + 8.
Out of the various LHS and RHS values, the LHS value and
RHS value is the same. So option 2 is the answer.
By using the base change formula, which states
The given equation is
By substituting the values of log 5 and log 3.
= 1.46